发表机构
Sandia National Laboratories; Massachusetts Institute of Technology（桑迪亚国家实验室; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出多保真度方法，在数据稀缺时通过分层或非分层策略利用低保真度数据构建三角输运映射，改进估计并提升下游推断中的条件采样与不确定性量化。
AI 中文摘要
我们开发了多保真度方法，用于在低保真度数据丰富而高保真度数据稀缺时，从样本构建三角输运映射。利用这组多保真度数据，我们近似一个三角输运映射，该映射在易于处理的参考密度与高保真度目标分布之间双射映射。我们引入了两种利用低保真度数据的策略：一种分层方法，组合相邻保真度级别之间的映射；以及一种非分层方法，通过保真度保持修正将低保真度信息纳入映射参数化。数值实验将这些策略与单保真度输运进行比较，并展示了所提出的多保真度方法如何从有限的高保真度数据中改进映射估计。为了说明学习到的映射的更广泛用途，我们还将它们部署在下游的摊销模拟推断任务中。这个例子表明，当高保真度数据稀缺时，多保真度改进的映射估计可以转化为改进的条件采样和不确定性量化。
英文摘要
We develop multifidelity methods for constructing triangular transport maps from samples, when high-fidelity data are scarce but lower-fidelity data are more abundant. Using this set of multifidelity data, we approximate a triangular transport map that bijectively maps between a tractable reference density and the high-fidelity target distribution. We introduce two strategies to leverage low-fidelity data: a hierarchical approach that composes maps between adjacent fidelity levels, and a non-hierarchical method that incorporates low-fidelity information through monotonicity-preserving corrections to the map parameterization. Numerical experiments compare these strategies with single-fidelity transport and demonstrate how the proposed multifidelity approaches can improve map estimation from limited high-fidelity data. To illustrate the broader utility of the learned maps, we also deploy them in a downstream amortized simulation-based inference task. This example shows that multifidelity improvements in map estimation can translate to improved conditional sampling and uncertainty quantification when high-fidelity data are scarce.
